About Optics & Photonics TopicsOSA Publishing developed the Optics and Photonics Topics to help organize its diverse content more accurately by topic area. This topic browser contains over 2400 terms and is organized in a three-level hierarchy. Read more.

Topics can be refined further in the search results. The Topic facet will reveal the high-level topics associated with the articles returned in the search results.

Abstract

Temporal phase shifting in automatic interferogram analysis offers very high accuracy of phase retrieval providing that several experimental conditions are met. The paper is focused on the calibration error of unequal phase changes across the interferogram field, i.e., tilt-shift error. For its detection the lattice-site representation of phase shift angles is proposed. The error can be readily discerned using (N+1) algorithms with the last frame overlapping the first one. Four and five frame algorithms are considered. The influence of experimental parameters on the error detection sensitivity is discussed. Numerical studies are complemented by experimental results.

Figures (20)

Phase shift angle histograms and their lattice-site representations calculated using Eqs. (1) and (2) for the case of tilt-shift error of 1.0 µrad. Tilt axis parallel to fringe direction. Left and right column results are for four and five frame algorithms, respectively. Upper row-conventional histograms, bottom row-lattice-site representations. Very similar results are obtained for the same tilt-shift error value for the perpendicular orientation of the tilt axis.

Phase shift angle histograms and lattice-site representations for the case of the tilt-shift error of 1.0 µrad. Tilt axis parallel to fringe direction. Nonlinear detection, γ≠1. Very similar results are obtained for the tilt axis perpendicular to fringe direction. Compare with Fig. 1.

Phase shift histograms and lattice-sites for two cases of constant phase steps of 70 deg (left) and 110 deg (right). Five frame data; tilt-shift error of 1 µrad, γ≠1. The results are almost the same for the beam tilt axis being parallel and perpendicular to fringe direction. Compare with Figs. 1 and 5.

Phase shift angle histograms and lattice-sites calculated using Eqs. (1) and (2) for the tilt-shift error of 1.0 µrad. Unequal phase steps between the frames (see text). Tilt axis parallel to fringe direction, γ=1. Very similar results are obtained for the same tilt-shift error value and perpendicular orientation of the tilt axis.

Phase shift angle histograms, upper row, and lattice-site representations, bottom row, calculated using Eq. (1) from two sets of four frames and one set of five component interferograms, Eq. (2). Null-fringe interferometer adjustment, nominally equal steps realized by three PZTs. See text for more detailed explanation.

Calculated phase shift angle histograms and lattice-sites for an experiment with an increased tilt-shift error and changed sign, realized by another PZT, as compared with the case of Fig. 16. Five frame lattice-site representation provides very good display of experimental errors (tilt-shift error, unequal phase steps and detection nonlinearity).